The present invention relates to an eccentric grinding machine with an eccentric gearing between its drive and its grinding disc. Such a machine comprising a grinding disk is known from DE-OS 36 09 441 (U.S. Pat. No. 4,759,152). It carries two toothed rims of different dimensioning on its rear side, which toothed rims abrade with varying degrees of intensity at the machined workpiece with rotational movement of different speeds. However, it is difficult to determine when the machine is running whether or not the eccentric grinding machine is producing a coarse or a fine grinding.